M Mathman87 Apr 2010 30 0 May 10, 2010 #1 Can anyone give an \(\displaystyle \epsilon\) - N proof that the sequence: xn = \(\displaystyle {\frac {2\,{n}^{2}+3}{4\,{n}^{2}+1}} \) tends to 1/2? Also more generally, give the \(\displaystyle \epsilon\) - N proof that the sequence {xn} n=1... infinity tends to x

Can anyone give an \(\displaystyle \epsilon\) - N proof that the sequence: xn = \(\displaystyle {\frac {2\,{n}^{2}+3}{4\,{n}^{2}+1}} \) tends to 1/2? Also more generally, give the \(\displaystyle \epsilon\) - N proof that the sequence {xn} n=1... infinity tends to x

P Plato MHF Helper Aug 2006 22,461 8,633 May 10, 2010 #2 If \(\displaystyle 0 < \varepsilon < 1\) let \(\displaystyle n > \frac{{\sqrt {\frac{5}{{2\varepsilon }} - 1} }}{2}\).

If \(\displaystyle 0 < \varepsilon < 1\) let \(\displaystyle n > \frac{{\sqrt {\frac{5}{{2\varepsilon }} - 1} }}{2}\).

M Mathman87 Apr 2010 30 0 May 10, 2010 #3 Ok, i worked it through and i can understand that answer. Im having trouble with the general proof however?

Ok, i worked it through and i can understand that answer. Im having trouble with the general proof however?